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Perimeter Institute Quantum Discussions

This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity.

Although entanglement constitutes one of the most remarkable differences between classical and quantum mechanics, and entanglement does have directly observable consequences, entanglement is not a regular observable like momentum or energy. It is rather a non-linear functional of a typically large set of such observables.

We explore the role of rotational symmetry of quantum key distribution
(QKD) protocols in their security. Specifically, in the first part of the
talk, we consider a generalized QKD protocol with discrete rotational
symmetry. Note that, before our work, each QKD protocol seems to have a
different security proof. Given that the techniques of those proofs are
similar, it will be interesting to have a unified proof for QKD protocols
with symmetry (e.g., the BB84 protocol and the SARG04 protocol). This is

Most modern discussions of Bell's theorem take microscopic causality (the arrow of time) for granted, and raise serious doubts concerning realism and/or relativity. Alternatively, one may allow a weak form of backwards-in-time causation, by considering "causes" to have not only "effects" at later times but also "influences" at earlier times. These "influences" generate the correlations of quantum entanglement, but do not enable information to be transmitted to the past. Can one realize this scenario in a mathematical model?

In this talk, I will show how to efficiently generate graph states
based on realistic linear optics (with imperfect photon detectors and source), how to do scalable quantum computation with probabilistic atom photon
interactions, and how to simulate strongly correlated many-body physics with ultracold atomic gas.

Complexity class MA is a class of yes/no problems for which the answer `yes\' has a short certificate that can be efficiently checked by a classical randomized algorithm. We prove that MA has a natural complete